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  • 1
    Digitale Medien
    Digitale Medien
    Fréchet Derivatives For Curved Interfaces In the Ray Approximation (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 97 (1989), S. 0 
    Details
    ISSN: 1365-246X
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie
    Notizen: The sensitivity of ray and beam theoretical seismograms to changes in velocity models and curved interfaces is discussed in this paper. Previous results from Nowack & Lutter (1988) give the derivatives of travel-time and ray amplitude with respect to changes of smoothly varying velocities. These derivatives are required to perform linearized maximum likelihood inversions for structure. In the ray approximation, smooth interfaces are incorporated by applying Snell's law locally, correcting wavefront curvature, and using local plane-wave reflection and transmission coefficients. the partial derivatives for travel-time are directly calculated along the original ray trajectory using Fermat's principle. For perturbations of the ray amplitude of a reflected/transmitted ray, the ray shift of the perturbed two-point ray trajectory must be accounted for. the approach followed here is to calculate the approximately perturbed two-point ray using perturbation theory without additional ray tracing. the perturbed ray amplitudes are then computed directly, including modified reflection/transmission coefficients and geometric spreading, along this approximate two-point ray. Several numerical experiments are conducted which invert for velocity and interface shape using both travel-time and amplitude in order to test the derived partial derivative operators. Travel-time and amplitude inversion results are also contrasted with amplitude being less sensitive to larger scale features and more sensitive to heterogeneity curvature.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-246X.1989.tb00519.x
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Wavefronts and solutions of the eikonal equation (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 110 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie
    Notizen: In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat's principle, first-order changes in the traveltime can be found by integrating along initial ray trajectories. Alternatively, linearized ray equations can be used to obtain perturbed rays for which traveltimes can be found. A comparison of the ray solution with approximate solutions for the traveltime is presented. The eikonal equation can also be solved directly without rays. This includes recent finite-difference methods for traveltimes. These methods avoid the ambiguity of multivalued time-fields by tracking only minimum traveltimes. The direct, numerical solution of the eikonal equation is illustrated by several examples using forward and reverse propagation of curved wavefronts. From these examples, it is shown that first-arrival wavefronts are generally non-reversible. This is relevant for tomographic applications which often use only first-arrival information. In order to obtain unique reverse propagation, multi-valued traveltimes must be accounted for. This is similar to difficulties encountered in traveltime inversion for 1-D structure when only first-arrivals are used.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00712.x
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Perturbation from isotropic to anisotropic heterogeneous media in the ray approximation (1991)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 106 (1991), S. 0 
    Details
    ISSN: 1365-246X
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie
    Notizen: In this paper, perturbation methods are used to obtain ray results in slightly anisotropic, heterogeneous media from a nearby isotropic medium. The advantage of this approach is that rays computed by available 2-D isotropic ray-tracing algorithms can be used to approximately compute, by perturbation, ray theoretical results in more general 3-D slightly anisotropic, heterogeneous media. The perturbation approach also makes possible an efficient computation of ray sensitivity operators necessary in seismic tomography studies. In order to compute approximate ray results for quasi-shear waves, degenerate perturbation theory must be used in order to split a single shear wave in an isotropic medium into two quasi-shear waves in a nearby anisotropic medium. The perturbation approach is tested on an effectively anisotropic model of aligned cracks within a linear, vertical velocity gradient. Perturbed traveltimes, ray paths and particle motions of quasi-compressional and quasi-shear waves for such an anisotropic medium are compared with exact ray results. Good agreement between the exact and perturbed results is found.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb04597.x
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Seismic attenuation values obtained from instantaneous-frequency matching and spectral ratios (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 123 (1995), S. 0 
    Details
    ISSN: 1365-246X
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie
    Notizen: In this paper, attenuation values are obtained from seismic data using instantaneous-frequency matching and spectral ratios. to obtain differential t* values using instantaneous-frequency matching, a near offset reference pulse is attenuated until the resulting instantaneous frequency matches the observed value at the receiver. Prior to matching, filtering can be applied to each trace in order to reduce the effects of noise on the calculated instantaneous frequencies. In the second method, the spectral ratio between a receiver pulse and a reference pulse is used to obtain differential t* values. to obtain an unbiased estimate, a variable spectral bandwidth is used depending on the noise level of the data. the two methods are tested using synthetic traces and then applied to crustal refraction data from the 1986 PASSCAL Ouachita experiment. Results show that the differential t* values obtained using filtered, instantaneous-frequency matching are consistent with and have less scatter than those obtained from spectral ratios with a variable bandwidth.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-246X.1995.tb06658.x
    Standort Signatur Erwartet Verfügbarkeit
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